Problem: What do the following two equations represent? $5x+y = 2$ $-5x+25y = -2$
Explanation: Putting the first equation in $y = mx + b$ form gives: $5x+y = 2$ $y = -5x+2$ Putting the second equation in $y = mx + b$ form gives: $-5x+25y = -2$ $25y = 5x-2$ $y = \dfrac{1}{5}x - \dfrac{2}{25}$ The slopes are negative inverses of each other, so the lines are perpendicular.